Hello Bev,
We have the 2 pieces of information, William has a Father named John, and William was of Peel.
Go onto the Imuseum website and bring up all the Baptisms for a William Watterson - between 1850 & 1870 eliminate the ones that don't have a John Father.
You are looking for a Baptism in - every parish, as sometimes the Baptism can be noted .- from Peel.
Then check out each William Watterson in the Census.
Averil